(705b) Closed-Loop Dynamic Real Time Optimization with a Stable MPC Formulation

Market conditions have continued to push for increasing economic improvement in process performance through automation. In the current hierarchy of the industrial process automation architecture, Dynamic Real Time Optimization (DRTO) is a supervisory strategy that computes optimal set-point trajectories for the lower level Model Predictive Control (MPC), typically based on the economics of the process. DRTO overcomes the shortcomings of a traditional RTO since it does not require the plant to attain steady state before execution and thus can be used for processes with frequent transitions.

In [7] the proposed DRTO strategy operates in an open-loop fashion without considering the presence of the control system. This leads to an assumption of perfect control that is not practically achievable and thus generates a sub-optimal performance. This was overcome by the closed-loop DRTO (CL-DRTO) formulation [1] in which MPC optimization subproblems are embedded into the DRTO layer, thereby establishing a multilevel dynamic optimization problem. The resulting multilevel dynamic optimization problem is then reformulated as a single level mathematical program with complementarity constraints (MPCC) where the MPC subproblems are replaced as constraints of the DRTO optimization using the KKT optimality conditions [2].

The MPC formulation considered in the previous study is limited to stable system dynamics. Various MPC formulations have been proposed to tackle the issue of stability. Some of these strategies include Equality constraints [5,6] and Lyapunov based MPC [4]. A brief review of the stability enforcing mechanisms is given in [3]. Incorporating these formulations into the CL-DRTO strategy can ensure applicability to both stable and unstable system dynamics.

Motivated by the above considerations, the present work will address incorporating stability constraints in the CL-DRTO. To this end, first an MPC formulation will be developed that readily handles achieving set point trajectory control for unstable systems. Subsequently, the stabilizing MPC formulation will be converted to equivalent KKT conditions, and incorporated as a part of the CL-DRTO. Closed-loop stability and optimality issues will be studied and simulations on a nonlinear CSTR will be utilized to illustrate the efficacy of the proposed approach.

References:

1. Jamaludin, M. Z., Swartz, C.L.E. Dynamic real-time optimization with closed-loop prediction, AIChE Journal, 63 3896-3911 (2017)
2. Jamaludin, M. Z., Swartz, C.L.E. Approximation of closed-loop prediction for dynamic real-time optimization calculations, Computers & Chemical Engineering, 103 23-38 (2017)
3. Mayne, D.Q., Rawlings, J.B, Rao, C.V., Scokaert, P.O.M. Constrained model predictive control: Stability and optimality, Automatica, 36 789-814 (2000)
4. P Mhaskar, NH El-Farra, PD Christofides , Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control, Systems & Control Letters, 55 650-659 (2006)
5. Rawlings, J.B., Muske, K.R. Model predictive control with linear models, AIChE Journal, 39 262-287 (1993)
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7. Tosukhowong, T., Lee, J.M., Lee, J.H., and Lu, J., An introduction to a dynamic plant-wide optimization strategy for an integrated plant. Comp. Chem. Eng., 29(1), 199-208 (2004)